Bath Box drainage all gone bad. HELP

Hi.
My husband and I have just completely reno'd our bathroom and now that we have installed the bath, done the tiling and jumped in for a shower we have made an embarrassing discovery....

water goes everywhere.

We installed a double ended bath into a bath box that we built, so basically there is a shelf all the way around the bath. We realise now that usually these tubs are only used as baths, not with showers overhead. A little late now.

Does anyone have any ideas on the best way to deal with the drainage issue. Water collects in the corner and runs off the sides of the bath

The only thing I can think of is to have that entire unit pitch one way, then install a drain in that corner. You would have to have a trap and a vent properly installed just like any other drain.
That's really kind of ghetto rigging it though. You can under mount a tub to get the effect that you were going for. You aren't going to find one in a plastic enclosure though.

When you take a shower water splashes all over the walls, right? At least it does on the short wall where the faucet and shower head is and also partially along the long wall. When the water lands outside the tub it is not going into the drain. You need to keep the deflected water from body inside the tub. Normally this type of bathtub setting is for a soaking tub. Maybe a hand held shower in lieu of a shower curtain? Or add a stand alone shower somewhere else.

Could you raise the tile be even with the highest ridge of the soaking tub, maybe angle slightly downward toward the tub? THen put a lip on the outer edge where the glass screen will go. Just thinking out loud to generate some ideas